Gravitational energy in stationary spacetimes
Abstract
Static observers remain on Killingvector worldlines and measure the restmass + kinetic energies of particles moving past them, and the flux of that mechanical energy through space and time. The total mechanical energy is the total flux through a spacelike cut at one time. The difference between the total mass energy and the total mechanical energy is the total gravitational energy, which we prove to be negative for certain classes of systems. For spherical systems, Misner, Thorne and Wheeler define the total gravitational energy in this way. To obtain the gravitational energy density analogous to that of electromagnetism we first use Einstein's equations with integrations by parts to remove secondorder derivatives. Next we apply a conformal transformation to reexpress the scalar 3curvature of the 3space. The resulting density is nonlocal. We repeat the argument for mechanical energies as measured by stationary observers moving orthogonally to constant time slices like the 'zero angular momentum' observers of Bardeen who exist even within ergospheres.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 December 2006
 DOI:
 10.1088/02649381/23/23/030
 arXiv:
 arXiv:grqc/0610052
 Bibcode:
 2006CQGra..23.7111K
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 Accepted for publication in Class. Quantum Grav